Electronic Journal of Probability

Convergence rates of Markov chains on spaces of partitions

Harry Crane and Steven Lalley

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We study the convergence rate to stationarity for a class of exchangeable partition-valued Markov chains called cut-and-paste chains. The law governing the transitions of a cut-and-paste chain are determined by products of i.i.d. stochastic matrices, which describe the chain induced on the simplex by taking asymptotic frequencies.  Using this representation, we establish upper bounds for the mixing times of ergodic cut-and-paste chains, and under certain conditions on the distribution of the governing random matrices we show that the "cutoff phenomenon" holds.

Article information

Electron. J. Probab., Volume 18 (2013), paper no. 61, 23 pp.

Accepted: 13 June 2013
First available in Project Euclid: 4 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 60B10: Convergence of probability measures 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52)

cut-and-paste chain mixing time exchangeability cutoff phenomenon Lyapunov exponent

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Crane, Harry; Lalley, Steven. Convergence rates of Markov chains on spaces of partitions. Electron. J. Probab. 18 (2013), paper no. 61, 23 pp. doi:10.1214/EJP.v18-2389. https://projecteuclid.org/euclid.ejp/1465064286

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